%I A061922
%S A061922 1,1,2,5,14,42,132,421,1382,4478,15580,54114,181676,650484,2289320,
%T A061922 8028901,28045302,103229014,372640460,1336511110,4882492452,
%U A061922 17534836812,63692926552,234287550818,868236370364,3281589811404
%N A061922 Xcatalans - produced as a self-convolved sequence like Catalan numbers 
               (A000108) but use carryless GF(2)[ X ] polynomial multiplication.
%C A061922 Shifts one place left when Xmult-convolved (XMULTCONV) with itself.
%p A061922 Xcatalans(30); Xcatalans := proc(upto_n) local a,i,k; a := [1]; for i 
               from 1 to upto_n do a := [ op(a), add(Xmult(a[k],a[i-k+1]), k=1..i)]; 
               od; RETURN(a); end;
%p A061922 XMULTCONV := proc(a,b) local c,i,k,n; n := min( nops(a), nops(b) ); c 
               := []; for i from 0 to n-1 do c := [ op(c), add(Xmult(a[k+1],b[i-k+1]), 
               k=0..i)]; od; RETURN(c); end;
%Y A061922 For Xmult, see A048720 (Xmult table) or A048631 (Xfactorials). Other 
               self-convolved sequences: A000108, A007460 - A007464, A025192.
%Y A061922 Sequence in context: A054392 A006930 A036767 this_sequence A162746 A148329 
               A024175
%Y A061922 Adjacent sequences: A061919 A061920 A061921 this_sequence A061923 A061924 
               A061925
%K A061922 nonn,easy,eigen
%O A061922 0,3
%A A061922 Antti Karttunen May 15 2001